Problem: Simplify the following expression: $x = \dfrac{6t^2 + 24t - 30}{t + 5} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $6$ , so we can rewrite the expression: $ x =\dfrac{6(t^2 + 4t - 5)}{t + 5} $ Then we factor the remaining polynomial: $t^2 + {4}t {-5} $ ${5} {-1} = {4}$ ${5} \times {-1} = {-5}$ $ (t + {5}) (t {-1}) $ This gives us a factored expression: $\dfrac{6(t + {5}) (t {-1})}{t + 5}$ We can divide the numerator and denominator by $(t - 5)$ on condition that $t \neq -5$ Therefore $x = 6(t - 1); t \neq -5$